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Proof step 1 from proof mult-02 (conclusion)

⊦ 0 ≤ i0 ∧ i0 < j ∧ 0 ≤ i ∧ 0 < j0 → (i * j + i0) / (j0 * j) = i / j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 ≤ i0, i0 < j, 0 ≤ i, 0 < j0, 0 < j ⊦ (i * j + i0) / (j0 * j) = i / j0

Rule argument

Additional information

Used simplifier rules: mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%numlef-01: ⊦ (* i) ≤ j → i - 1 < j; (forward) from specification int-abs%numlsf-02: ⊦ (* i) < j → i + 1 ≤ j; (forward) from specification int-abs